Answer:
The vertex form of a quadratic function is given by:
h(x) = a(x - h)^2 + k
where (h, k) represents the coordinates of the vertex.
In this case, the graph of h is a translation 4 units right and 1 unit down from the graph of f(x) = x^2, which means the vertex of h is obtained by shifting the vertex of f(x) = x^2 by 4 units to the right and 1 unit down.
The vertex of f(x) = x^2 is (0, 0). Shifting it 4 units right gives the x-coordinate of the new vertex as 4, and shifting it 1 unit down gives the y-coordinate as -1.
Therefore, the vertex of h is (4, -1). Plugging these values into the vertex form equation, we have:
h(x) = a(x - 4)^2 - 1
So, the function h(x) in vertex form with a translation of 4 units right and 1 unit down is h(x) = a(x - 4)^2 - 1.
